Chebyshev Constants

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

The constants

$$\lambda_{m,n} = \inf_{r\in R_{m,n}} \sup_{x\geq 0} \vert e^{-x}-r(x)\vert,$$

where

$$r(x)={p(x)\over q(x)},$$

$p$ and $q$ are $m$th and $n$th order Polynomials, and $R_{m,n}$ is the set all Rational Functions with Real coefficients.

See also One-Ninth Constant, Rational Function

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/onenin/onenin.html

Petrushev, P. P. and Popov, V. A. Rational Approximation of Real Functions. New York: Cambridge University Press, 1987.

Varga, R. S. Scientific Computations on Mathematical Problems and Conjectures. Philadelphia, PA: SIAM, 1990.

Philadelphia, PA: SIAM, 1990.